We discuss the role of instantons in the spectroscopy of ordinary and exotic hadrons as well as in high energy reactions. We argue that the instanton induced flavor- and spin-dependent quark-quark and quark-gluon interactions can explain many features of the hadron spectrum. The observed anomalous spin and flavor effects in various reactions with hadrons can also be understood within the instanton model for QCD vacuum.
Heavy hadrons are analyzed in a random and dilute gas of instantons. We derive the instanton-induced interactions between heavy and light quarks at next to leading order in the heavy quark mass and in the planar approximation, and discuss their effects on the hadronic spectrum. The role of these interactions in the formation of exotic hadrons is also discussed.
In this work we present the results from numerical simulations of an interacting ensemble of instanton-dyons in the $SU(3)$ gauge group with $N_f=2$ flavors of massless quarks. Dynamical quarks are included via the effective interactions induced by the fermionic determinant evaluated in the subspace of topological zero modes. The eigenvalue spectrum of the Dirac operator is studied at different volumes to extract the chiral condensate and eigenvalue gap, with both observables providing consistent values of the chiral transition temperature $T_c$. We find that a sufficient density of dyons is r…
By means of the functional integral method we show that in the case of the quark-antiquark pairing at zero temperature and zero chemical potential (in the vacuum) the singlet pairing is more preferable than that with the color-flavor locking (CFL)
The instanton--anti-instanton pair induced asymptotics of perturbation theory expansion for the cross section of electron--positron pair annihilation to hadrons and hadronic width of $τ$-lepton was found. For $N_f = N_c$ the nonperturbative instanton contribution is finite and may be calculated without phenomenological input. The instanton induced peturbative asymptotics was shown to be enhanced as $(n+10)!$ and in the intermediate region $n<15$ may exceed the renormalon contribution. Unfortunately, the analysis of $\sim 1/n$ corrections shows that for $n \sim 10$ the obtained asymptotic expre…
We estimate the twist-4 spin-1 nucleon matrix element f_2 in an instanton-based description of the QCD vacuum. In addition to the flavor-nonsinglet we compute also the flavor-singlet matrix element, which appears in next-to-leading order of the (1/N_c)-expansion. The corresponding twist-3 spin-2 matrix elements d_2 are suppressed in the packing fraction of the instanton medium, (\bar ρ)/(\bar R) << 1. We use our results to estimate the leading (1/Q^2) power corrections to the first moment of the proton and neutron spin structure functions G_1, as well as the intrinsic charm contribution to the…
A large body of evidence from lattice calculations indicates that instantons play a major role in the physics of light hadrons. This evidence is summarized, and recent results concerning the instanton content of the SU(3) vacuum, instanton contributions to the static potential, and a new class of instanton solutions at finite temperature are reviewed.
Roles of instantons in strangeness hadron physics are discussed. After introducing general features of instantons, hadron spectroscopy under the influence of instanton-quark effective interactions is discussed. Emphases are on the H dibaryon, spin-orbit splittings of P-wave baryons and baryon-baryon interactions and spectrum of the pentaquarks.
We compute the effect of small-size instanton corrections to current-current correlators, for all combinations of axial, vector, and possibly flavour non-diagonal currents. We apply our result to the hadronic decays of the $τ$ lepton, in order to assess the reliability of the determination of $\as$ from the $τ$ hadronic width.
"Exotic quarks" in the title refers to a modification of quark periodicity condition on the thermal circle by introduction of some phases -- known also as "flavor holonomies" -- different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them one can dramatically modify both phase transitions. In the language of instanton constituents -- instanton-dyons or monopoles -- it has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes betwe…
We review our recent study of the role played by the chiral interactions induced by instantons, in the lowest-lying sector of the light hadron spectrum. We discuss how the ordering of the lowest meson and baryon excitations is explained by the structure of the instanton-induced quark-quark and gluon-gluon interaction. We focus on the pion, nucleon, vector- and axial-vector mesons, and on the scalar glueball. We find that all these hadrons are bound in this model and have realistic masses.
These are the (twice) extended notes of a set of lectures given at the ``12th Workshop on Hadronic Interactions'' at the IF/UERJ, Rio de Janeiro (31. 5. - 2. 6. 2000). The lectures aim at introducing essential concepts of instanton physics, with emphasis on the role of instantons in generating tunneling amplitudes, vacuum structure, and the induced quark interactions associated with the axial anomaly. A few examples for the impact of instantons on the physics of hadrons are also mentioned.
Recently it was shown that in QCD-like theories with $N_f > N$, where $N_f$ is the number of light flavors and $N$ is the number of colors, there are correlation functions that vanish in perturbation theory and at short distances receive dominant, calculable contributions from small instantons. Here we extend the set of such objects to theories with $N_f = N$, which includes real QCD, and discuss their application as a calibration of lattice computations at small quark mass. We revisit the related issue of the $u$ quark mass and its additive renormalization by small instantons, and discuss an …
Chiral quark model with a broken-U(3) flavor symmetry can be interpreted as the effective theory of the instanton-dominated non-perturbative QCD. This naturally suggests the possibility of a negative singlet/octet coupling ratio, which has been found, in a previous publication, to be compatible with the phenomenological description of the nucleon spin-flavor structure.
We describe quenched spectroscopy in SU(2) gauge theory using smoothed gauge field configurations. We investigate the properties of quarks moving in instanton background field configurations, where the sizes and locations of the instantons are taken from simulations of the full gauge theory. By themselves, these multi-instanton configurations do not confine quarks, but they induce chiral symmetry breaking.
QCD instantons are arguably the best motivated yet unobserved nonperturbative effects predicted by the Standard Model. A discovery and detailed study of instanton-generated processes at colliders would provide a new window into the phenomenological exploration of QCD and a vastly improved fundamental understanding of its non-perturbative dynamics. Building on the optical theorem, we numerically calculate the total instanton cross-section from the elastic scattering amplitude, also including quantum effects arising from resummed perturbative exchanges between hard gluons in the initial state, t…
We investigate the effects of flavor SU(3)-symmetry breaking on the quark, gluon, and mixed quark-gluon condensates, based on the nonlocal effective chiral action from the instanton vacuum. We employ two different parameterizations for the dependence of the momentum-dependent dynamical quark mass on the strange current quark mass. With a proper choice of the current-quark mass dependence of the dynamical quark mass, we show that the gluon condensate is independent of the current quark mass. We obtain the ratios of the quark and mixed condensates, respectively: $[<\bar{s}s>/< \bar{u}u>]^{1/3}=0…
We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.
Effects of the spin orbit-force on hadronic systems with strangeness or charm are investigated by a valence quark model with the instanton-induced interaction. By introducing this interaction, the spin-orbit splittings in the negative-parity hyperons becomes 0.14 -- 0.37 times smaller. The flavor-octet baryon mass spectrum and the splittings in the charmed baryons become consistent with the experiments. Though the splitting is also reduced in the flavor-singlet baryons, it still gives two third of the experimental value. The reduction comes from the cancellation between the one-gluon exchange …
Instantons generate strong non-perturbative interactions between quarks. In the vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300-400 MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as $\sim$~100 MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two fla…
We phenomenologically study whether partonic collisions responsible for the growth of hadron-hadron cross sections at high energy can be ascribed to instanton-induced processes. Although non-perturbative in nature, these interactions occur at the semi-hard scale $Q\sim 1-2$ GeV, and should therefore be described using information from deep inelastic leptonic scattering on the partonic constituents in nucleons, pions, and photons. After considering shadowing corrections in nucleon-nucleon scattering, we fix a free instanton tail suppression parameter and determine the effective quark-quark cros…
We investigate the twist-3 pion and kaon distribution amplitudes of the pseudoscalar (phi^p_{pi,K}) and pseudotensor (phi^{sigma}_{pi,K}) types, based on the effective chiral action from the instanton vacuum. Effects of flavor SU(3) symmetry breaking are explicitly taken into account. The Gegenbauer moments and the moments of the distribution amplitudes (<xi^m>) are also computed. Our results are summarized as follows: a^p_{2,pi} ~ 0.4, a^p_{1,K} ~ 0.02 and a^p_{2,K} ~ 0.14, and a^{sigma}_{2,pi} ~ 0.02 and a^{sigma}_{1,K} ~ a^{sigma}_{2,K} ~ 0; <xi^2>^p_π ~ <xi^2>^p_K ~ 0.37 and <xi>^p_K ~ 0, …
Inspired by a recent proposal for a Higgs description of QCD we study the possible formation of a color-octet/flavor-octet quark-anti-quark condensate in the instanton liquid model. For this purpose we calculate two-point correlation functions of color-singlet and octet quark-anti-quark operators. We find long range order in the standard $<\barψψ>$ channel, but not in the color-octet channel. We emphasize that similar calculations in lattice QCD can check whether or not a color-flavor locked Higgs phase is realized in QCD at zero temperature and baryon density.
In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge field and quark induced interactions between instantons we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the groundstate. In the physical case of two light and one…
Instanton liquid model being effective model of the QCD vacuum describes well the hadrons at low as well at intermediate energies. Thus, contact with perturbative QCD results is possible providing the unique information about the quark-gluon distribution functions in the QCD vacuum and hadrons at low energy normalization point. As an illustrative example we consider the pion transition form factor for the process $γ^*γ^*\to π^0$ at space-like values of photon momenta. The leading and next-to-leading order power asymptotics of the form factor and the relation between the light-cone pion distrib…
The instanton interaction in QCD generates an effective potential for scalar quark-antiquark condensates in the color singlet and octet channels. For three light quark flavors the cubic term in this potential induces an octet condensate and ``spontaneous breaking'' of color in the vacuum. Realistic masses of the rho- and eta'-mesons are compatible with renormalization-group-improved instanton perturbation theory.
QCD instantons generate non-perturbative spin- and flavor- dependent forces between quarks. We review the results of a series of studies on instanton-induced correlations in hadrons. We first present some evidence for instanton-mediated interactions in QCD, based on lattice simulations. Then we show that the Instanton Liquid Model can reproduce the available data on proton and pion form factors at large momentum transfer and explain the delay of the onset of the perturbative regime in several hard reactions. We also show that instantons generate a deeply bound scalar color anti-triplet diquark…
We study b, c quark hadronization from QGP. We obtain the yields of charm and bottom flavored hadrons within the statistical hadronization model. The important novel feature of this study is that we take into account the high strangeness and entropy content of QGP, conserving strangeness and entropy yields at hadronization.
Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks in instanton field allows simultaneously to explain some important features of low- and high- energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavy-quark potential are briefly discussed within the instanton liquid model.
This is the first of a sequence of papers that address the non-perturbative origin of the central, and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center of mass frame. We suggest a "dense instanton ensemble" model for the QCD vacuum, to explain the interquark forces in mesons, from quarkonia to heavy-light and light-light ones, to the extent it is possible. The sequels will show how to export these interactions to the light front, and derive the corresponding Hamiltonians and mesonic wavefunctions.
We investigate the relevance of the instanton-induced determinantal 't Hooft interaction to the eta-nucleon coupling within the framework of a three-flavor linear sigma model in the OZI-rule-respecting basis. Instantons, in combination with the spontaneous breaking of chiral symmetry, are shown to provide the major mechanism for the ideal mixing between pseudoscalar strange and non-strange quarkonia. As long as 't Hooft's interaction captures most of the basic features of the axial QCD gluon anomaly, we identify the anomaly as the main culprit for the appearance of octet flavor symmetry in the…
Motivated by measurements of the flavor singlet axial coupling constant of the nucleon in polarized deep inelastic scattering we study the contribution of instantons to OZI violation in the axial-vector channel. We consider, in particular, the f_1-a_1 meson splitting, the flavor singlet and triplet axial coupling of a constituent quark, and the axial coupling constant of the nucleon. We show that instantons provide a short distance contribution to OZI violating correlation functions which is repulsive in the f_1 meson channel and adds to the flavor singlet three-point function of a constituent…
We study hadronic correlation functions in the interacting instanton liquid model, both at zero and nonzero temperature $T$. At zero $T$ we investigate the dependence of the correlators on the instanton ensemble, in particular the effect of the fermionic determinant. We demonstrate that quark-induced correlations between instantons are important, especially in the repulsive $η'$ and $δ$-meson channels. We also calculate a large number of mesonic and baryonic correlation functions as a function of temperature. We find three different types of behavior as $T\to T_c$. The vector channels $ρ,a_1,Δ…
Heavy flavor measurements in high multiplicity proton-proton and proton-nucleus collisions at collider energies enable unique insights into their production and hadronization mechanism because experimental and theoretical uncertainties cancel in ratios of their cross-sections relative to minimum bias events. We explore such event engineering using the Color Glass Condensate (CGC) effective field theory to compute short distance charmonium cross-sections. The CGC is combined with heavy-quark fragmentation functions to compute $D$-meson cross-sections; for the $J/ψ$, hadronization is described e…
I address the question of how much of QCD in the chiral limit is reproduced by instantons. After reconstructing the instanton content of smoothed Monte Carlo lattice configurations, I compare hadron spectroscopy on this instanton ensemble to the spectroscopy on the original ``physical'' smoothed configurations using a chirally optimised clover fermion action. By studying the zero mode zone in simple instances I find that the optimised action gives a satisfactory description of it. Through the Banks-Casher formula, instantons by themselves are shown to break chiral symmetry but hadron correlato…
Heavy flavor production at the future Electron-Ion Collider (EIC) will allow us to precisely determine the quark/gluon fragmentation processes in vacuum and the nuclear medium especially within the poorly constrained kinematic region. Heavy flavor hadron and jet reconstruction with the recent EIC detector design have been studies in simulation. Results of corresponding physics projections such as the flavor dependent hadron nuclear modification factor $R_{eA}$ in electron+nucleus collisions will be shown. The statistical precision obtained by these proposed heavy flavor measurements for the fu…
We consider QCD instanton-induced contributions to lepton pair production in hadron-hadron collisions. We relate these contributions to those known from deep inelastic scattering and demonstrate that they can be calculated reliably for sufficiently large momentum transfer. We observe that the instanton contribution to the angular distribution of the lepton pairs at finite momentum transfer strongly violates the Lam-Tung relation - a relation between coefficient functions of the angular distribution which is valid within the framework of ordinary perturbation theory. The drastic violation of th…
It is a common belief that the last missing piece of the Standard Model of particles physics was found with the discovery of the Higgs boson at the Large Hadron Collider. However, there remains a major prediction of quantum tunnelling processes mediated by instanton solutions in the Yang-Mills theory, that is still untested in the Standard Model. The direct experimental observation of instanton-induced processes, which are a consequence of the non-trivial vacuum structure of the Standard Model and of quantum tunnelling in QFT, would be a major breakthrough in modern particle physics. In this p…
We study how vortices in dense superfluid hadronic matter can connect to vortices in superfluid quark matter, as in rotating neutron stars, focusing on the extent to which quark-hadron continuity can be maintained. As we show, a singly quantized vortex in three-flavor symmetric hadronic matter can connect smoothly to a singly quantized non-Abelian vortex in three-flavor symmetric quark matter in the color-flavor locked (CFL) phase, without the necessity for boojums appearing at the transition.
We study nonperturbative flavor correlations between pairs of leading and next-to-leading charged hadrons within jets at the Electron-Ion Collider (EIC). We introduce a charge correlation ratio observable $r_c$ that distinguishes same- and opposite-sign charged pairs. Using Monte Carlo simulations with different event generators, $r_c$ is examined as a function of various kinematic variables for different combinations of hadron species, and the feasibility of such measurements at the EIC is demonstrated. The precision hadronization study we propose will provide new tests of hadronization model…
We study the role of semi-classical QCD vacuum solutions in high energy scattering by considering the instanton contribution to hadronic cross sections. We propose a new type of instanton-induced interactions (``instanton ladder'') that leads to the rising with energy hadronic cross section of Regge type (the Pomeron). We argue that this interaction may be responsible for the structure of the soft Pomeron. The intercept is calculated. It has a non-analytic dependence on the strong coupling constant, allowing a non-singular continuation into the non-perturbative region. We derive the Pomeron tr…
Both in heavy-ion collisions as in magnetars very strong magnetic fields are produced, which has its influence on the phases of matter involved. In this paper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e = 1.7 x 10^19 G) on the chiral symmetry restoring phase transition using the Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions depends on the relative magnitude of the magnetic field and the instanton interaction strength. We study two specific regimes in the phase diagram, high chemical potential and zero temperature and vice versa, which a…
We compute the axial vector current, form factor, and coupling for quarks in the instanton liquid model with two light flavors. Non-local current corrections are derived, as required by the effective 't Hooft interaction. We obtain a pion-mediated axial form factor and an axial coupling which, when simply applied in the non-relativistic limit for constituent quarks, matches the experimental value to within a few percent, both in and out of the chiral limit.
We have studied the directed flow of light-flavor hadrons for Au + Au collisions at $\sqrt{S_{NN}}=$ 7.7 - 200 GeV. The initial condition is taken from a suitable Glauber model which is further evolved within the framework of relativistic hydrodynamics. Model calculations of the rapidity-odd directed flow ($v_1$) of identified light-flavor hadrons are compared with the available experimental data after suitably calibrating the initial condition to describe the rapidity dependence of charged particle multiplicity and net-proton yield. For reasonable choice of the initial condition, we are able …
We demonstrate a holographic realization of color-flavor locking phase, using N=4 SU(Nc) SYM coupled to N=2 Nf fundamental hypermultiplets as an example. The gravity dual consists of Nc D3-branes and Nf D7-branes with world volume gauge field representing the baryon density. Treating a small number \tilde{N}c << Nc of D3-branes as Yang-Mills instantons on the D7-branes, we consider possible potential(s) on their moduli space or equivalently the Higgs branch. We show that a non-trivial potential can be generated by including the backreaction of the baryonic density on the D7-branes, this dynami…
We study instanton effects on $B \rightarrow X_sγ$ decay using the heavy quark effective field theory and the operator product expansion. In the dilute gas approximation the effect is negligibly small. This is in contrast to the result of the instanton effect in inclusive semileptonic $b\rightarrow u$ decay but similar to the inclusive hadronic $τ$ decay. We discuss the similarities and differences of the $B \rightarrow X_sγ$ decay compared to inclusive hadronic $τ$ decay and semileptonic $B$ decay.
We study the scaled-energy (x_B) distribution of bottom-flavored hadrons (B) inclusively produced in top-quark decays at next-to-leading order (NLO) in the general-mass variable-flavor-number scheme endowed with realistic, nonperturbative fragmentation functions that are obtained through a global fit to e^+e^- data from CERN LEP1 and SLAC SLC exploiting their universality and scaling violations. Specifically, we study the effects of gluon fragmentation and finite bottom-quark and B-hadron masses. We find the NLO corrections to be significant. Gluon fragmentation leads to an appreciable reducti…
This is the second paper of the series aimed at understanding the ensemble of instanton-dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, $(det T)^{N_f}$ and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 and 128 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density.
We investigate the kaon semileptonic decay (K_{l3}) form factors within the framework of the nonlocal chiral quark model from the instanton vacuum, taking into account the effects of flavor SU(3) symmetry breaking. We also consider the problem of gauge invariance arising from the momentum-dependent quark mass in the present work. All theoretical calculations are carried out without any adjustable parameter, the average instanton size (rho ~ 1/3 fm) and the inter-instanton distance (R ~ 1 fm) having been fixed. We also show that the present results satisfy the Callan-Treiman low-energy theorem …
In the past decade, exotic hadrons with charm and bottom flavors have been extensively studied both in experiments and in theories. In this review, we provide topical discussions by selecting $X,Y,Z$ particles, to which Belle has made important contributions. These are $X(3872)$, $Y(4260)$, $Z_c(4430)^+$, $Z_c(3900)^+$, $Z_{b}(10610)^+$ and $Z_{b}(10650)^+$. Based on the current experimental observations, we discuss those states with emphasis on hadronic molecule whose dynamics is governed by chiral symmetry and heavy-quark symmetry of QCD. We also mention briefly various interpretations and s…
We use a variant of the $D4$-$D8$ construction that includes two chiral and one heavy meson, to describe heavy-light baryons and their exotics as heavy mesons bound to a flavor instanton in bulk. At strong coupling, the heavy meson is shown to {\it always bind} in the form of a flavor instanton zero mode in the fundamental representation. The ensuing instanton moduli for the heavy baryons exhibits both chiral and heavy quark symmetry. We detail how to quantize it, and derive model independent mass relations for heavy bayons with a single-heavy quark in leading order, in overall agreement with …
We summarize recent progress in the theoretical description of heavy-flavored-hadron inclusive production at next-to-leading order in the general-mass variable-flavor-number scheme. Specifically, we discuss the influence of finite-mass effects on the determination D-meson fragmentation functions from a global fit to e^+e^- annihilation data and on the transverse-momentum distribution of B-meson hadroproduction. We also demonstrate that the fixed-flavor-number scheme, implemented with up-to-date parton density functions and strong-coupling constant, provides a surprisingly good description of B…
We discuss the stability of hidden and open heavy-flavor hadronic states made of either two or three mesons. References are made in passing to studies regarding two and three-body systems containing baryons. We perform a comparative study analyzing the results in terms of quark and hadron degrees of freedom. Compact and molecular states are found to exist in very specific situations. We estimate the decay width for the different scenarios: weak decays for bound states by the strong interaction, and strong decays for hadronic resonances above a decay threshold. The experimental observation of n…
We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with equal number of colors $N_c$ and flavors $N_f$. We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2, 3$. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry b…
